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Kane's 22nd minute header against Southampton at Wembley on Tuesday took him past Alan Shearer's previous record, which was set when he played for Blackburn in 1995.
The 24-year-old admitted he was keen to break Shearer's record after he moved level with the former England star with a hat-trick in Tottenham's win at Burnley on Saturday.
Kane now has 22 goals for Tottenham in all competitions this season.